Iterative Proportional Fitting

Adjust sampling weights to given totals based on household-level and/or individual level constraints.

ipf(
  dat,
  hid = NULL,
  conP = NULL,
  conH = NULL,
  epsP = 1e-06,
  epsH = 0.01,
  verbose = FALSE,
  w = NULL,
  bound = 4,
  maxIter = 200,
  meanHH = TRUE,
  allPthenH = TRUE,
  returnNA = TRUE,
  looseH = FALSE,
  numericalWeighting = computeLinear,
  check_hh_vars = TRUE,
  conversion_messages = FALSE,
  nameCalibWeight = "calibWeight",
  minMaxTrim = NULL
)

Arguments

dat	a `data.table` containing household ids (optionally), base weights (optionally), household and/or personal level variables (numerical or categorical) that should be fitted.
hid	name of the column containing the household-ids within `dat` or NULL if such a variable does not exist.
conP	list or (partly) named list defining the constraints on person level. The list elements are contingency tables in array representation with dimnames corresponding to the names of the relevant calibration variables in `dat`. If a numerical variable is to be calibrated, the respective list element has to be named with the name of that numerical variable. Otherwise the list element shoud NOT be named.
conH	list or (partly) named list defining the constraints on household level. The list elements are contingency tables in array representation with dimnames corresponding to the names of the relevant calibration variables in `dat`. If a numerical variable is to be calibrated, the respective list element has to be named with the name of that numerical variable. Otherwise the list element shoud NOT be named.
epsP	numeric value or list (of numeric values and/or arrays) specifying the convergence limit(s) for `conP`. The list can contain numeric values and/or arrays which must appear in the same order as the corresponding constraints in `conP`. Also, an array must have the same dimensions and dimnames as the corresponding constraint in `conP`.
epsH	numeric value or list (of numeric values and/or arrays) specifying the convergence limit(s) for `conH`. The list can contain numeric values and/or arrays which must appear in the same order as the corresponding constraints in `conH`. Also, an array must have the same dimensions and dimnames as the corresponding constraint in `conH`.
verbose	if TRUE, some progress information will be printed.
w	name if the column containing the base weights within `dat` or NULL if such a variable does not exist. In the latter case, every observation in `dat` is assigned a starting weight of 1.
bound	numeric value specifying the multiplier for determining the weight trimming boundary if the change of the base weights should be restricted, i.e. if the weights should stay between 1/`bound``w` and `bound``w`.
maxIter	numeric value specifying the maximum number of iterations that should be performed.
meanHH	if TRUE, every person in a household is assigned the mean of the person weights corresponding to the household. If `"geometric"`, the geometric mean is used rather than the arithmetic mean.
allPthenH	if TRUE, all the person level calibration steps are performed before the houshold level calibration steps (and `meanHH`, if specified). If FALSE, the houshold level calibration steps (and `meanHH`, if specified) are performed after everey person level calibration step. This can lead to better convergence properties in certain cases but also means that the total number of calibration steps is increased.
returnNA	if TRUE, the calibrated weight will be set to NA in case of no convergence.
looseH	if FALSE, the actual constraints `conH` are used for calibrating all the hh weights. If TRUE, only the weights for which the lower and upper thresholds defined by `conH` and `epsH` are exceeded are calibrated. They are however not calibrated against the actual constraints `conH` but against these lower and upper thresholds, i.e. `conH`-`conH``epsH` and `conH`+`conH``epsH`.
numericalWeighting	See numericalWeighting
check_hh_vars	If `TRUE` check for non-unique values inside of a household for variables in household constraints
conversion_messages	show a message, if inputs need to be reformatted. This can be useful for speed optimizations if ipf is called several times with similar inputs (for example bootstrapping)
nameCalibWeight	character defining the name of the variable for the newly generated calibrated weight.
minMaxTrim	numeric vector of length2, first element a minimum value for weights to be trimmed to, second element a maximum value for weights to be trimmed to.

Value

The function will return the input data dat with the calibrated weights calibWeight as an additional column as well as attributes. If no convergence has been reached in maxIter steps, and returnNA is TRUE (the default), the column calibWeights will only consist of NAs. The attributes of the table are attributes derived from the data.table class as well as the following.

`converged`	Did the algorithm converge in `maxIter` steps?
`iterations`	The number of iterations performed.
`conP`, `conH`, `epsP`, `epsH`	See Arguments.
`conP_adj`, `conH_adj`	Adjusted versions of `conP` and `conH`
`formP`, `formH`	Formulas that were used to calculate `conP_adj` and `conH_adj` based on the output table.

Details

This function implements the weighting procedure described here. Usage examples can be found in the corresponding vignette (vignette("ipf")).

conP and conH are contingency tables, which can be created with xtabs. The dimnames of those tables should match the names and levels of the corresponding columns in dat.

maxIter, epsP and epsH are the stopping criteria. epsP and epsH describe relative tolerances in the sense that $$1-epsP < \frac{w_{i+1}}{w_i} < 1+epsP$$ will be used as convergence criterium. Here i is the iteration step and wi is the weight of a specific person at step i.

The algorithm performs best if all varables occuring in the constraints (conP and conH) as well as the household variable are coded as factor-columns in dat. Otherwise, conversions will be necessary which can be monitored with the conversion_messages argument. Setting check_hh_vars to FALSE can also incease the performance of the scheme.

Author

Alexander Kowarik, Gregor de Cillia

Examples

if (FALSE) {

# load data
eusilc <- demo.eusilc(n = 1, prettyNames = TRUE)

# personal constraints
conP1 <- xtabs(pWeight ~ age, data = eusilc)
conP2 <- xtabs(pWeight ~ gender + region, data = eusilc)
conP3 <- xtabs(pWeight*eqIncome ~ gender, data = eusilc)

# household constraints
conH1 <- xtabs(pWeight ~ hsize + region, data = eusilc)

# simple usage ------------------------------------------

calibweights1 <- ipf(
  eusilc,
  conP = list(conP1, conP2, eqIncome = conP3),
  bound = NULL,
  verbose = TRUE
)

# compare personal weight with the calibweigth
calibweights1[, .(hid, pWeight, calibWeight)]

# advanced usage ----------------------------------------

# use an array of tolerances
epsH1 <- conH1
epsH1[1:4, ] <- 0.005
epsH1[5, ] <- 0.2

# create an initial weight for the calibration
eusilc[, regSamp := .N, by = region]
eusilc[, regPop := sum(pWeight), by = region]
eusilc[, baseWeight := regPop/regSamp]

calibweights2 <- ipf(
  eusilc,
  conP = list(conP1, conP2),
  conH = list(conH1),
  epsP = 1e-6,
  epsH = list(epsH1),
  bound = 4,
  w = "baseWeight",
  verbose = TRUE
)

# show an adjusted version of conP and the original
attr(calibweights2, "conP_adj")
attr(calibweights2, "conP")
}